“It is with tremendous sadness that we announce the death of our beautiful, dynamic and one-of-a-kind mother,” the statement said.
The British-born writer, sister of actress Joan Collins, died in Los Angeles, her spokeswoman said.
Collins’s career spanned four decades and she sold more than 500 million books in 40 countries.
The family statement said the writer lived “a wonderfully full life”, adored by family, friends and readers.
“She was a true inspiration, a trailblazer for women in fiction and a creative force. She will live on through her characters but we already miss her beyond words,” it added.
Collins was diagnosed with stage-four breast cancer six-and-a-half years ago, according to US celebrity magazine People.
Her sister Joan, 82, told People magazine she was “completely devastated”.
“She was my best friend. I admire how she handled this. She was a wonderful, brave and a beautiful person and I love her,” she said.
Jackie Collins began writing as a teenager, making up racy stories for her schoolfriends, according to a biography on her website.
Her first novel, The World is Full of Married Men, was published in 1968 and became a scandalous bestseller. It was banned in Australia and branded “disgusting” by romance writer Barbara Cartland.
In 1985, her novel Hollywood Wives was made into a mini-series by ABC, starring Anthony Hopkins and Candice Bergen.
In a 2011 interview with the Associated Press, Collins said that she “never felt bashful writing about sex”.
“I think I’ve helped people’s sex lives,” she said.
“Sex is a driving force in the world so I don’t think it’s unusual that I write about sex. I try to make it erotic, too.”